Solving/Factoring Polynomials

Solve By Factoring

100

12x³-3x²=0

x={0, 1/4}

200

2x³-3x²-32x+48=0

x={-4, 3/2 ,4}

300

2x⁴=9x²

x={0, =(3sqrt2)/2 , -(3sqrt2)/2}

400

x³+3x²=24x+72

x= {-3 , +/- 2sqrt6}

500

2x³-5x²+40x-100=0

x={ 5/2 , +/- 2isqrt5}

Difference of Squares

100

9x²-25

(3x+5)(3x-5)

200

n²-4

(n+2)(n-2)

300

72c⁶-2

2(6c³+1)(6c³-1)

400

100w⁵-100w

100w(w²+1)(w-1)(w+1)

500

7x⁷y-28xy³

7xy(x³-2y)(x³+2y)

Sum/Difference of Cubes

100

x³+27

(x+3)(x²-3x+9)

200

24m³n+375mn³

3mn(2m+5n)(4m²-10mn+25n²)

300

216x³+125

(6x+5)(36x²-30x+25)

400

8x³ – 27

(2x-3)(4x²+6x+9)

500

2x³+128y³

2(x+4y)(x²-4xy+16y²)

Grouping

100

Factor:

2x³-3x²-32x+48

(x-4)(x+4)(2x-3)

200

x³+2x²+5x+10=0

(x²+5)(x+2)

300

Factor

2x³-5x²+40x-100

(x²+20)(2x-5)

400

Factor:

x³+3x²=24x+72

(x²-24)(x+3)

500

x³-x²+9x-9

(x²+9)(x-1)

Trinomials

100

x²+x-20

(x+5)(x-4)

200

2a³+38a²+68a

2a(a+17)(a+2)

300

n⁴+2n²-24

(n²+6)(n+2)(n-2)

400

x⁵-24x³-25x

x(x+5)(x-5)(x²+1)

500

9m⁴-12m²+4

(3m²-2)(3m²-2)    or    (3m²-2)²